Line and angle proofs | |
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Description | |
Exercise Name: | Line and angle proofs |
Math Missions: | High school geometry Math Mission |
Types of Problems: | 2 |
The Line and angle proofs exercise appears under the High school geometry Math Mission. This exercise uses lines and angles to establish facts via rigorous proof.
Types of Problems[]
There are two types of problems in this exercise:
- Fill in the spaces to complete the proof: This problem has a proof of a statement with missing spaces. The student is asked to use the included diagram to fill in the template with statements that will complete the proof correctly.
- Select the best reasoning: This problem makes a true claim. The student is asked to select which line of reasoning best establishes the fact that is being claimed from a multiple choice list.
Strategies[]
Knowledge of line and angle theorems being proved would assist with accuracy and efficiency, but generally only basic definitions are needed to ensure success on this exercise.
- Complementary angles add up to and supplementary angles add up to .
- The last line of a proof is generally the statement that was supposed to be proved.
- A complement to an angle that measures is , and a supplement is .
- Some of the proofs call upon the triangle congruence theorems (for example, SAS or SSS).
Real-life Applications[]
- Understanding the relationships between angles is important in drafting, mapping and architecture.
- Engineers and architects use angles for designs, roads, buildings and sporting facilities.
- Athletes use angles to enhance their performance. Carpenters use angles to make chairs, tables and sofas.
- Artists use their knowledge of angles to sketch portraits and paintings.